Stewart6e3_2 - MATH 191, Sections 1 and 3 Calculus I Fall...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 191, Sections 1 and 3 Calculus I Fall 2007 Section 3.2: The Product and Quotient Rules Lets continue amassing shortcuts for computing derivatives. Weve now got rules for differentiating powers, as well as constant multiples, sums, and dif- ferences of functions whose derivatives we already know. We even know the derivative of an exponential function f ( x ) = e x ! Whats missing? Well, lots. Products, for one. Lets examine d dx ( f g ), and see if we can get a nice formula. Sadly, its not what we might immediately expect. First, a motivating Example. Consider the numbers 4 and 7, whose product is 4 7 = 28. What happens if we add a very small quantity, say 1 , to 4, and another small quan- tity, 2 , to 7, and then recompute the product? We now get (4 + 1 )(7 + 2 ) = . This expression represents the value to which the product 4 7 has been changed corresponding to a small change in those values. Whats most interesting here are those two cross-terms in the middle. If we think of 4 and 7 as the valuesare those two cross-terms in the middle....
View Full Document

Page1 / 6

Stewart6e3_2 - MATH 191, Sections 1 and 3 Calculus I Fall...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online